As a first step, we built a toy model of a gene regulatory network consisting of a small number of genes that positively or negatively regulate one another. By computer simulations, we found that a simple network can produce multiple stable states. We also found that a few rules imposed on the network can cause unidirectional transition of one network state to another. This mimics unidirectional transition of cell states during cell differentiation. Using extended computer simulations, we are currently further investigating dynamic behaviors of gene regulator networks. We are also testing the possibility that our computational model can simulate the global gene expression profiles obtained by DNA microarray analysis of differentiating mouse embryonic stem cells.